Regulators as Feedback

Part 9 · Voltage Regulation

Key point: the divider sets \(V_{\mathrm{OUT}}\). FB stays at \(V_{\mathrm{ref}}\). Loop gain \(K\) is what makes \(Z_{\mathrm{out}}\) small.

\(V_{\mathrm{set}}=V_{\mathrm{ref}}(1+R_{\mathrm{top}}/R_{\mathrm{bot}})\). Closed, \(Z_{\mathrm{out}}=R_{\mathrm{out}}/(1+K)\). Open, \(K=0\).

1
Closed. Droop is 24 mV.
Preset 1.2 V ref · 3.3 V. Loop closed. Vset is 3.30 V. VOUT is 3.28 V. FB is 1.19 V. Zout is 59 mΩ. DC droop is 24 mV. F = 0.364. K = 32 dB. FB ≈ Vref. Divider sets VOUT. Load step is Rout/(1+K).
2
Vset is 5.00 V.
Preset 1.25 V · 5.0 V. Loop closed. Vset is 5.00 V. VOUT is 4.98 V. FB is 1.24 V. Zout is 59 mΩ. DC droop is 24 mV. F = 0.250. K = 32 dB. The figure shows Vref 1.25 V. FB ≈ Vref. Divider sets VOUT. Load step is Rout/(1+K).
3
Open. VOUT is 10.8 V.
Preset Loop open. Loop open. Vset is 3.30 V. VOUT is 10.8 V. FB is 3.94 V. Zout is 2.40 Ω. DC droop is 0.96 V. FB cut. Pass FET is a dropper. Load step is I·Rout.
4
12 dB. VOUT is 3.06 V.
Preset Weak 12 dB. Loop closed. Vset is 3.30 V. VOUT is 3.06 V. FB is 1.11 V. Zout is 482 mΩ. DC droop is 0.24 V. F = 0.364. K = 12 dB. The figure shows Vref 1.20 V. The VOUT trace ends below the ±5% band. FB is off Vref. Divider sets VOUT. Load step is Rout/(1+K).
5
42 dB. Droop is 9 mV.
Preset Tight 42 dB. Loop closed. Vset is 3.30 V. VOUT is 3.29 V. FB is 1.20 V. Zout is 19 mΩ. DC droop is 9 mV. F = 0.364. K = 42 dB. The figure shows Vref 1.20 V. FB ≈ Vref. Divider sets VOUT. Load step is Rout/(1+K).

Enough VIN that this page stays out of dropout. One pole, \(R_{\mathrm{out}}C_{\mathrm{out}}\). \(K\) is a single DC gain. Phase margin is a later page. Part 11 uses duty in place of this pass FET.

P · C · F on an LDO

Closed: FB tracks \(V_{\mathrm{ref}}\). Open: the pass FET is a dropper. Load step at 80 µs.

\(V_{\mathrm{ref}}\) (V) \(R_{\mathrm{top}}\) (kΩ) \(R_{\mathrm{bot}}\) (kΩ) Error-amp \(K\) (dB) \(\Delta I\) (A) \(R_{\mathrm{out}}\) of \(P\) (Ω)

LDO · blue pass \(P\) · amber error amp \(C\) · teal divider \(F\) · violet \(V_{\mathrm{ref}}\)

VOUT · load step at 80 µs · band is \(V_{\mathrm{set}}\) ±5%

FB and \(V_{\mathrm{ref}}\) · same load step

V_set—

VOUT—

FB—

Z_out—

DC droop—

\(V_{\mathrm{set}}=V_{\mathrm{ref}}(1+R_{\mathrm{top}}/R_{\mathrm{bot}})\)

→ —

\(F=R_{\mathrm{bot}}/(R_{\mathrm{top}}+R_{\mathrm{bot}})\)

→ —

\(Z_{\mathrm{out}}=R_{\mathrm{out}}/(1+K)\)

→ —

\(\Delta V=\Delta I\,Z_{\mathrm{out}}\)

→ —